Difference between revisions of "Val's Wacky Equation"

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The next step is to add up all those reciprocals from the individual lists. The more lists a game appears on, and the higher its rank, the higher this number will be. This is also where the limiter becomes important. Let's say there were 5 lists, and everybody voted a certain game #1. Then we'd have this happening:
 
The next step is to add up all those reciprocals from the individual lists. The more lists a game appears on, and the higher its rank, the higher this number will be. This is also where the limiter becomes important. Let's say there were 5 lists, and everybody voted a certain game #1. Then we'd have this happening:
 
   
 
   
<div align="center">[[Image:ValRank5.png]]</div>
+
<div align="center">[[Image:ValRank4.png]]</div>
 
   
 
   
 
So the highest possible total a game can have a this point is 1. Without the limiter, a game could have a score higher than 1 at this point, which would cause some wonky things in the next step.
 
So the highest possible total a game can have a this point is 1. Without the limiter, a game could have a score higher than 1 at this point, which would cause some wonky things in the next step.
 
   
 
   
<div align="center">[[Image:ValRank4.png]]</div>
+
<div align="center">[[Image:ValRank5.png]]</div>
 
   
 
   
  
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So that's how the ranking system was designed. I hope someone out there enjoyed reading this.
 
So that's how the ranking system was designed. I hope someone out there enjoyed reading this.
 
  
 
== Why Averaging Isn't a Good Option ==
 
== Why Averaging Isn't a Good Option ==

Revision as of 11:01, 28 September 2009

Have you ever wondered how Val's mind works?

Well, he gave us some insight when he explained how the top 100 NES & SNES games were ranked.

The Equation


Those of you who have read through the Top 100 SNES list, and possibly the Top 100 NES list, might be wondering how we came to the final ordering for these games. Well, each game received a score from 1 to 1000 based on it's position on each individual list, and was then ranked against all other games with the highest scoring game getting the top spot.

- Valdronius


Simple Version .... LOL You won't understand it

Now you may be wondering how each games score was calculated. Well, to put it simply:

ValRank0.png

Where n is the number of individual lists the game appeared on,

x is the game's position on an individual list,

and l is the total number of individual lists.

Breaking down the equation

For those of you who haven't taken university mathematics, I shall go into a more detailed explanation of each step along the way. (For those of you who have, I apologize for using 1.n, it just looks nicer than 1 + n/10).

Alright, let's start from the inside and work our way out. For clarity, from here out when I use the term 'rank', I'm referring to a games rank on an individual list.

ValRank1.png

The first thing we do is take the reciprocal of the games rank. If I rated one game 15th on my list, and another game 30th, it wouldn't make sense to give them 15 points and 30 points respectively, as we wanted the 15th ranked game to be higher on the final list. So we take the reciprocal of each number to achieve the desired result. 1/15 = 0.067, 1/30 = 0.033.

ValRank2.png

Before we take the reciprocal, we want to add what I call a 'limiter' to the games rank. The limiter is the total number of individual lists, less 1. It might not be immediately clear why this is necessary, so let's move forward.

ValRank3.png

The next step is to add up all those reciprocals from the individual lists. The more lists a game appears on, and the higher its rank, the higher this number will be. This is also where the limiter becomes important. Let's say there were 5 lists, and everybody voted a certain game #1. Then we'd have this happening:

ValRank4.png

So the highest possible total a game can have a this point is 1. Without the limiter, a game could have a score higher than 1 at this point, which would cause some wonky things in the next step.

ValRank5.png


Finally we have a booster. When a game appears on multiple lists, it gets a boost for the number of lists it appears on. So again, if there are 5 lists, a game could receive a low boost of 1.1 for being on 1 list, up to 1.5 for appearing on 5 lists. If you want to see why I had to use the limiters, take the 1.5th root of 2, and the 1.1th root of 2. For this system we would want the former to be higher, but you'll see that this is not the case. When the numbers are between 0 and 1, this achieves the desired effect.

Well, that was fairly long-winded. Let's walk through an example to see how A Link to the Past scored. There were 7 lists in total, and it was ranked 6, 1, 1, 4, 2, 2, and 4. Then we'll get this:

ValRank6.png

Multiplying the number at the end by 1000 is purely for aesthetic reasons. It is easier to rank numbers that range from 1 to 1000 than it is to rank numbers ranging from 0 to 1. To show that the booster does indeed work the way it is supposed to, let's take the 1.1th root of 0.8190476. This results in 0.834 or a score of 834.

So that's how the ranking system was designed. I hope someone out there enjoyed reading this.

Why Averaging Isn't a Good Option

It's just not. Trust us.

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